Curve Ball: Baseball, Statistics, and the Role of Chance in the Game

Just finished this excellent book by Jim Albert and Jay Bennet originally published in 2001 but updated after the 2002 season. This book starts out with a discussion of models that tabletop baseball games such as Cadaco All Star Baseball, APBA, and Strat-o-Matic use. The authors then go on to discuss statistical models and how they apply to baseball. I'll summarize some of their interesting (although not all of them definitive) conclusions:

Chance plays a larger role in baseball statistics than most people think. For example, using simple confidence intervals if a player has a .422 OBP in 682 plate appearances you can only conclude with 95% confidence that his true ability to get on base falls between .385 and .459. As a result, regression to the mean always needs to be considered when evaluating a player based on a single season. (chapter 3)

There is no general effect for the situational stats that break down a player's performance by half seasons, day and night, and grass versus turf (chapter 4)

Home/road differences, ground ball/fly ball differences, and hitting against the opposite handed pitcher show evidence of a general effect where the differences are +12 points, +12 points against groundball pitchers, and +15 points against the opposite hand respectively. In other words, these effects are roughly the same for everyone. Some players may have truly enhanced ability in such situations but it is not typical. (chapter 4)

Hitting in a specific pitch count and hitting with runners on base show some evidence for differences based on ability. Particularly the former where high homerun/strikeout hitters hit worse when down in the count. (chapter 4)

There is some evidence that some hitters may be streaky (chapter 5)

RC/G more accurately predicts team runs/game than other systems including TA (Total Average), BRA (Base Run Average) , OPS (On base + slug), DX (Scoring Index), SLG, OBP, and AVG. In fact, the accuracy of these systems is reflected in the order. Note that AVG is the least predictive but the stat that most baseball fans follow. It would be interesting to see how Extrapolated Runs would figure in this analysis. (chapter 6)

The authors then use regression to come up with their own system that is slightly more accurate that RC/G (Least Squares Linear Regression). Interestingly, their system is derived directly from team data from 1871 to 1999 while Runs Created is an intuitive calculation (chapter 7). They then go on to show how their model is basically the Linear Weights system developed by Pete Palmer based on ideas originally put forward by George Lindsey in 1963. Interestingly, Lindsey and Palmer's system were developed based on run production probabilities in the 24 base-out situations. Originally Lindsey used partial data from the 1959 and 1960 seasons while Palmer ran computer simulations. The regression model, however, overvalues sacrifice flys while the Linear Weights System seems to overvalue stolen bases. (chapter 7)

The authors go on to show that RC/G tends to be a little unrealistic (overvaluing) for players at either end of the offensive spectrum. By inserting the player in the context of an average team this bias goes away and essentially mimics the Linear Weights model. (chapter 8)

The authors include a great Run Potential Table from 2002

Outs/Bases	0	1	2	3	1,2	1,3	2,3	1,2,3
0	.511	.896	1.142	1.405	1.511	1.838	1.956	2.332
1	.272	.536	0.682	0.944	0.936	1.185	1.358	1.510
2	.101	.227	0.322	0.363	0.450	0.524	0.633	0.776

They then include a probabality of scoring table from Lindsey's 1959 and 1960 data (I can't seem to find a more recent version of a table like this although the authors showed that Lindsey's data in general was fairly close to more recent compilation although Lindsey's sample size is not that large since there were only 16 teams during that era):

Outs/Bases	0	1	2	3	1,2	1,3	2,3	1,2,3
0	.253	.396	0.619	0.880	0.605	0.870	0.820	0.820
1	.145	.266	0.390	0.693	0.429	0.633	0.730	0.697
2	.067	.114	0.212	0.262	0.209	0.283	0.332	0.329

With this data it is relatively easy to evaluate when to steal bases, when to bunt, and when to intentionally walk a batter. In short they find that stealing 2nd base is advantageous as long as the runner has a probability of success of greater than 60%. Of course, the probability threshold goes down (into to the low 50s) in the later innings when the team is simply trying to score 1 run. This is interesting since most common wisdom I've always heard says that the SB % needs to be around 67% to be effective.

For bunting the conclusion is that only weak hitters should bunt in the early innings (per MoneyBall and most other sabermetric research) and otherwise bunting should only be done in late innings when the objective is to score a single run.

For intentional walks they used Barry Bonds as the test case and calculated that walking Bonds only makes sense with a runner on 2nd and 2 outs or 1st and 2nd with 2 outs (using 2002 data). Other situations either definitely call for pitching to him or are too close to call statistically. (chapter 8)

The authors include an interesting table on the probability of the home team winning given a score differential after each inning (again from Lindsey's data). For example, given a 3-0 lead after 7 innings the home team should win 94% of the time (much to the Cubs chagrin after game 6 of the NLCS). They use this data to weight the contribution of each play a player makes. This kind of analysis will be common with the increase in play by play data. This will lead to a true picture of each player's contribution to winning games. It would be nice if STATS, Inc. or MLB would make this data freely available (retrosheet only has 1992 and prior data). (chapter 10)

The authors include a table constructed from their own model for the odds of teams of various abilities getting a wild card birth, winning their division, pennant, and world series. In short they note that an average team (.483 to .517 winning percentage) should be expected to get into the playoffs 19% of the time. So it is not suprising that a Wild Card team would win the World Series. (chapter 12)

In all, this is a great exploration of some of the core sabermetric concepts.

Incidentally, the tables and formulas provided by the authors vindicate my earlier rant about Dusty Baker bunting in the early innings of the NLCS. The situation was Lofton on 1st nobody out, Grudzlienack batting. If Grudz attempts to bunt the probability of scoring is 36.5% calculated as p of scoring = ((ps * pss) + (pf * pfs)) where ps is the probability of a successful sacrifice, pss is the probability of scoring with a runner on 2nd and 1 out, pf is the probability of the sacrifice failing and pfs is the probability of scoring with a runner on 1st and 2 outs. So (.8 * .390) + (.2 * .266) = .365. If Grudz does not bunt the probabilty of scoring is 40.4% (including calculating a double play). This calculation is performed simply by calculating Grudz odds of walking, hitting a single etc. and then multiplying that by the probability of scoring at least one run in the base-out situation that results and then adding the products.

Maybe not a huge difference but bunting also takes the Cubs out of the big inning moving the run potential from .896 to .682. A no-win situation. Of course in 2003 the three teams with the lowest number of sacrifices hits were the Blue Jays (11), A's (22), and Red Sox (24). All 3 of these teams have sabermetric minded GM's. Not suprisingly, the Cardinals led the NL with 87. I wonder if that will change with their new emphasis on sabermetrics per an earlier post.